Calculus, 12 credits

Analys i en variabel, 12 hp

TAIU10

Main field of study

Mathematics Applied Mathematics

Course level

First cycle

Course type

Programme course

Examiner

Magnus Berggren

Director of studies or equivalent

Jesper Thorén

Education components

Preliminary scheduled hours: 202 h
Recommended self-study hours: 118 h
Possible deviation from course syllabus/programme syllabus
ECV = Elective / Compulsory / Voluntary
Course offered for Semester Period Timetable module Language Campus ECV
6IKEA Chemical Analysis Engineering, B Sc in Engineering 1 (Autumn 2017) 0, 1, 2 -, 4, 4 Swedish Linköping, Valla C
6IDAT Computer Engineering, B Sc in Engineering 1 (Autumn 2017) 0, 1, 2 -, 4, 4 Swedish Linköping, Valla C
6IELK Engineering Electronics, B Sc in Engineering 1 (Autumn 2017) 0, 1, 2 -, 4, 4 Swedish Linköping, Valla C
6IMAS Mechanical Engineering, B Sc in Engineering 1 (Autumn 2017) 0, 1, 2 -, 4, 4 Swedish Linköping, Valla C

Main field of study

Mathematics, Applied Mathematics

Course level

First cycle

Advancement level

G1X

Course offered for

  • Computer Engineering, B Sc in Engineering
  • Engineering Electronics, B Sc in Engineering
  • Chemical Analysis Engineering, B Sc in Engineering
  • Mechanical Engineering, B Sc in Engineering

Entry requirements

Note: Admission requirements for non-programme students usually also include admission requirements for the programme and threshold requirements for progression within the programme, or corresponding.

Intended learning outcomes

That you as a student will learn to feel confident with the mathematical expressions, reasoning and relations from Single Variable Calculus and that it will teach you calculating and problem solving skills needed for your further studies. After a completed course you should be able to:

  • Read and interpret mathematical texts
  • Explain definitions and expressions like local extremes, limits, continuity, derivatives, primitive functions and integrals
  • Explain and use central theorems like The Fundamental Theorem of Calculus, Mean-Value Theorems, The Intermediate-Value Theorem and The Max-Min Theorem.
  • Use mathematical laws for limits of functions, derivatives, antiderivatives and integrals.
  • Perform investigations of functions using derivatives, limits and the properties of basic functions and from this draw conclusions regarding the properties of the functions
  • Use standard techniques to calculate antiderivatives and definite integrals.
  • Express and calculate geometrical quantities like areas of plane regions, arc length, volumes of solids of revolution and areas of solids of revolution.
  • Handle differential equations (first-order separable and first-order linear equations and constant-coefficient equations of higher order.) and integralequations.
  • Explain Taylor’s formula
  • Use Taylorexpansions to approximate functions and investigate limits.
  • Perform checks of results and calculations to verify that they are correct and reasonable

Course content

  • Preparatory course: Equations and systems of equations. Geometric and arithmetic sums. Inequalities. Binomial theorem. Exponential functions and logarithms. Polynomials. Trigonometry and trigonometric functions.
  • Calculus: Real and complex numbers. Induction. Functions of a real variable. Elementary functions. Sequences, limits. Derivatives and continuity. Rules for differentiation. Properties of continuous functions. Study of functions. Primitive functions. Integration and geometrical applications, including area, curve length, areas of rotation and volumes of rotation. Improper integrals. Taylor's formula. Maclaurin expansions of elementary functions with applications to the calculation of limits. Linear ordinary differential equations of first and second order, separable equations.

    Teaching and working methods

    The course is taken during the first semester of the first year. Teaching is done in lectures and problem classes. The examination consists of two written tests.
    The course runs over the entire autumn semester.

    Examination

    KTR3Examination0 creditsU, 3, 4, 5
    KTR2Examination0 creditsU, 3, 4, 5
    KTR1Examination0 creditsU, 3, 4, 5
    TEN2Written examination6 creditsU, 3, 4, 5
    TEN1Written examination6 creditsU, 3, 4, 5
    Passed written test 1 and written test 2 gives a bonus on the first written examination (TEN1). Approved written test 3 gives a bonus to the second written examination (TEN2). The right to count the bonuses from the tests is 12 months from the date of writing.

    Grades

    Four-grade scale, LiU, U, 3, 4, 5

    Other information

    Supplementary courses: Transform Methods, Discrete Mathematics, Numerical Algorthms

    Department

    Matematiska institutionen

    Director of Studies or equivalent

    Jesper Thorén

    Examiner

    Magnus Berggren

    Course website and other links

    http://www.mai.liu.se/kurser/TAIU10-ing.html

    Education components

    Preliminary scheduled hours: 202 h
    Recommended self-study hours: 118 h

    Course literature

    Additional literature

    Books

    • Forsling, Göran och Neymark Mats, (2011) Matematisk analys, en variabel Liber
    • Code Name Scope Grading scale
    KTR3 Examination 0 credits U, 3, 4, 5
    KTR2 Examination 0 credits U, 3, 4, 5
    KTR1 Examination 0 credits U, 3, 4, 5
    TEN2 Written examination 6 credits U, 3, 4, 5
    TEN1 Written examination 6 credits U, 3, 4, 5
    Passed written test 1 and written test 2 gives a bonus on the first written examination (TEN1). Approved written test 3 gives a bonus to the second written examination (TEN2). The right to count the bonuses from the tests is 12 months from the date of writing.

    Regulations (apply to LiU in its entirety)

    The university is a government agency whose operations are regulated by legislation and ordinances, which include the Higher Education Act and the Higher Education Ordinance. In addition to legislation and ordinances, operations are subject to several policy documents. The Linköping University rule book collects currently valid decisions of a regulatory nature taken by the university board, the vice-chancellor and faculty/department boards.

    LiU’s rule book for education at first-cycle and second-cycle levels is available at http://styrdokument.liu.se/Regelsamling/Innehall/Utbildning_pa_grund-_och_avancerad_niva. 

    Student rights and obligations (login required)
    Linköping University common rules and regulations (in Swedish)

    Additional literature

    Books

    Forsling, Göran och Neymark Mats, (2011) Matematisk analys, en variabel Liber

    Download

    Note: The course matrix might contain more information in Swedish.

    I = Introduce, U = Teach, A = Utilize
    I U A Modules Comment
    1. DISCIPLINARY KNOWLEDGE AND REASONING
    1.1 Knowledge of underlying mathematics and science (G1X level)
    X
    X
    X
    TEN1
    		 
    
                                		
                        
    
                        
    
                            
                            1.2 Fundamental engineering knowledge (G1X level)
                            
                                
     
    
                                		
                            
                                
     
    
                                		
                            
                                
     
    
                                		
                            
                            
                            
                                
    
                                		
                        
    
                        
    
                            
                            1.3 Further knowledge, methods, and tools in one or several subjects in engineering or natural science (G2X level)
                            
                                
     
    
                                		
                            
                                
     
    
                                		
                            
                                
     
    
                                		
                            
                            
                            
                                
    
                                		
                        
    
                        
    
                            
                            1.4 Advanced knowledge, methods, and tools in one or several subjects in engineering or natural sciences (A1X level)
                            
                                
     
    
                                		
                            
                                
     
    
                                		
                            
                                
     
    
                                		
                            
                            
                            
                                
    
                                		
                        
    
                        
    
                            
                            1.5 Insight into current research and development work
                            
                                
     
    
                                		
                            
                                
     
    
                                		
                            
                                
     
    
                                		
                            
                            
                            
                                
    
                                		
                        
    
                        
                    
                        
    
                            
                                2. PERSONAL AND PROFESSIONAL SKILLS AND ATTRIBUTES
                            
                        
    
                        
                    
                        
    
                            
                            2.1 Analytical reasoning and problem solving
                            
                                
    X
    
                                		
                            
                                
    X
    
                                		
                            
                                
    X
    
                                		
                            
                                  
    TEN1
    
                                		
                            
                                
    
                                		
                        
    
                        
    
                            
                            2.2 Experimentation, investigation, and knowledge discovery
                            
                                
     
    
                                		
                            
                                
     
    
                                		
                            
                                
    X
    
                                		
                            
                            
                            
                                
    
                                		
                        
    
                        
    
                            
                            2.3 System thinking
                            
                                
     
    
                                		
                            
                                
     
    
                                		
                            
                                
     
    
                                		
                            
                            
                            
                                
    
                                		
                        
    
                        
    
                            
                            2.4 Attitudes, thought, and learning
                            
                                
     
    
                                		
                            
                                
    X
    
                                		
                            
                                
    X
    
                                		
                            
                                  
    TEN1
    
                                		
                            
                                
    
                                		
                        
    
                        
    
                            
                            2.5 Ethics, equity, and other responsibilities
                            
                                
     
    
                                		
                            
                                
     
    
                                		
                            
                                
     
    
                                		
                            
                            
                            
                                
    
                                		
                        
    
                        
                    
                        
    
                            
                                3. INTERPERSONAL SKILLS: TEAMWORK AND COMMUNICATION
                            
                        
    
                        
                    
                        
    
                            
                            3.1 Teamwork
                            
                                
     
    
                                		
                            
                                
     
    
                                		
                            
                                
     
    
                                		
                            
                            
                            
                                
    
                                		
                        
    
                        
    
                            
                            3.2 Communications
                            
                                
     
    
                                		
                            
                                
     
    
                                		
                            
                                
    X
    
                                		
                            
                            
                            
                                
    
                                		
                        
    
                        
    
                            
                            3.3 Communication in foreign languages
                            
                                
     
    
                                		
                            
                                
     
    
                                		
                            
                                
     
    
                                		
                            
                            
                            
                                
    
                                		
                        
    
                        
                    
                        
    
                            
                                4. CONCEIVING, DESIGNING, IMPLEMENTING AND OPERATING SYSTEMS IN THE ENTERPRISE, SOCIETAL AND ENVIRONMENTAL CONTEXT
                            
                        
    
                        
                    
                        
    
                            
                            4.1 External, societal, and environmental context
                            
                                
     
    
                                		
                            
                                
     
    
                                		
                            
                                
     
    
                                		
                            
                            
                            
                                
    
                                		
                        
    
                        
    
                            
                            4.2 Enterprise and business context
                            
                                
     
    
                                		
                            
                                
     
    
                                		
                            
                                
     
    
                                		
                            
                            
                            
                                
    
                                		
                        
    
                        
    
                            
                            4.3 Conceiving, system engineering and management
                            
                                
     
    
                                		
                            
                                
     
    
                                		
                            
                                
     
    
                                		
                            
                            
                            
                                
    
                                		
                        
    
                        
    
                            
                            4.4 Designing
                            
                                
     
    
                                		
                            
                                
     
    
                                		
                            
                                
     
    
                                		
                            
                            
                            
                                
    
                                		
                        
    
                        
    
                            
                            4.5 Implementing
                            
                                
     
    
                                		
                            
                                
     
    
                                		
                            
                                
     
    
                                		
                            
                            
                            
                                
    
                                		
                        
    
                        
    
                            
                            4.6 Operating
                            
                                
     
    
                                		
                            
                                
     
    
                                		
                            
                                
     
    
                                		
                            
                            
                            
                                
    
                                		
                        
    
                        
                    
                        
    
                            
                                5. PLANNING, EXECUTION AND PRESENTATION OF RESEARCH DEVELOPMENT PROJECTS WITH RESPECT TO SCIENTIFIC AND SOCIETAL NEEDS AND REQUIREMENTS
                            
                        
    
                        
                    
                        
    
                            
                            5.1 Societal conditions, including economic, social, and ecological aspects of sustainable development for knowledge development
                            
                                
     
    
                                		
                            
                                
     
    
                                		
                            
                                
     
    
                                		
                            
                            
                            
                                
    
                                		
                        
    
                        
    
                            
                            5.2 Economic conditions for knowledge development
                            
                                
     
    
                                		
                            
                                
     
    
                                		
                            
                                
     
    
                                		
                            
                            
                            
                                
    
                                		
                        
    
                        
    
                            
                            5.3 Identification of needs, structuring and planning of research or development projects
                            
                                
     
    
                                		
                            
                                
     
    
                                		
                            
                                
     
    
                                		
                            
                            
                            
                                
    
                                		
                        
    
                        
    
                            
                            5.4 Execution of research or development projects
                            
                                
     
    
                                		
                            
                                
     
    
                                		
                            
                                
     
    
                                		
                            
                            
                            
                                
    
                                		
                        
    
                        
    
                            
                            5.5 Presentation and evaluation of research or development projects
                            
                                
     
    
                                		
                            
                                
     
    
                                		
                            
                                
     
    
                                		
                            
                            
                            
                                
    
                                		
                        
    
                        
            
    
        
    

    

            
    
        
    
            

    
        
    
            
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